In electronics a NOT gate is more commonly called an inverter. The circle on the symbol is called a bubble, and is used in logic diagrams to indicate a logic negation between the external logic state and the internal logic state (1 to 0 or vice versa).
A weather watch, on the other hand, typically refers to an alert issued to indicate that conditions are favorable for the development of dangerous weather patterns, although the dangerous weather conditions themselves are not currently present.
A tornado watch means that conditions are favourable for the development of severe weather including tornadoes. This is issued over both land and water. A warning means that a tornado or funnel cloud is reported or is likely over land.